Abstract
The experiment of Pound & Repka shows that light undergoes a frequency shift in the gravitational field of the earth in accordance with General Relativity. Conversely, in the static case, we can use only the observed frequency shifts to define the gravitational field, presupposing the (constant) 3-geometry of the 3-space slices is known. The latter can be probed in principle by rigid rods, but more elegantly by the light geometry as developed by Abramowicz, shortly reviewed here. Our optical definition is independent of the theory of relativity. However, in the second part, we show that, in the static case, it coincides with the predictions for the acceleration of test particles in General Relativity. For the non-static case, our definition of gravity is no substitute for that one given in General Relativity. However, the static case is sufficient for certain discussions about the validity of the Principle of Equivalence.
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REFERENCES
Nieto, M. M., and Goldman, T. (1991). Phys. Rep. 205, 221.
Hönl, H. (1965). Phys. Bl. 21, 16.
Lemke, J., Mielke, E. W., and Hehl, F. W. (1994). Physik in unserer Zeit, 25, 36.
Lämmerzahl, C. (1998). Acta Physica Polonica B29, 1057.
Lämmerzahl, C. (1996). General Relativity and Gravitation 28, 1043.
Audretsch, J., and Lämmerzahl, C. (1988). Classical and Quantum Gravity 5, 1285.
Nowotny, E. (1972). Commun. Math. Phys. 26, 321.
L. Parker, (1983). In Proceedings of the Third Marcel Grossmann Meeting on General Relativity, Hu Ning, ed. (North-Holland, Amsterdam), p. 343.
Enders, A., and Nimtz, G. (1993). Phys. Rev. E 48, 632.
Steinberg, A. M., and Chiao, R. Y. (1994). Phys. Rev. A 49, 3283.
Weyl, H. (1919). Ann. d. Phys. 59, 101.
Straumann, N. (1987). Phys. Bl. 43, 414.
Morrison, P., and Gold, T. (1957). Essays on Gravity, (Gravity Research Foundation, New Boston, New Hampshire), p. 45.
Morrison, P. (1958). Am. J. Phys. 26, 358.
Ebner, D., and Dehnen, H. (1993). Phys. Bl. 49, 1013.
Dehnen, H., and Ebner, D. (1996). Foundations of Physics 26, 105.
Thieberger, P. (1965). N. Cim. 35, 358.
Beall, E. (1970). Phys. Rev. D 1, 961.
Pound, R., and Rebka, G. (1960). Phys. Rev. Lett. 4, 337.
Landau, L. D., and Lifshitz, E. M. Course of Theoretical Physics, Vol. II, Classical Theory of Fields (Pergamon Press, New York).
Abramowicz, M. A., Carter, B., and Lasota, J. P. (1988). 'Optical Reference Geometry for Stationary and Static Dynamics', Gen. Rel. Grav. 20, 1173–1183.
Abramowicz, M. A. (1992). 'Relativity of inwards and outwards: an example', Mon. Not. R. Astr. Soc. 256, 710–718.
Abramowicz, M. A., Lanza, A., Miller, J. C., and Sonego, S. (1997). 'Curving Newtonian Space', Gen. Rel. Grav. 29, 1585–1596.
Kristiansson, S., Sonego, S., and Abramowicz, M. A. (1998). 'Optical Space of the Reissner-Nordström Solutions', Gen. Rel. Grav. 30, 275–288.
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Ebner, D.W. Optical Definition of Gravity Under Static Conditions. General Relativity and Gravitation 33, 1147–1164 (2001). https://doi.org/10.1023/A:1012029216696
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DOI: https://doi.org/10.1023/A:1012029216696